Which of these two is correct, and why?
- two kinds of televisions
- two kinds of television
Assuming you're specifically interested in talking about television, (as opposed to whether one uses plural or singular nouns after "two kinds of" in general), it depends on context.
"Two kinds of televisions" would refer to different kinds of television sets, as in "We have two kinds of televisions: color and black-and-white."
"Two kinds of television" could refer to different kinds of televised programming, as in, "Programming for kids and programming for adults are two kinds of television."
Compare countable and uncountable definitions of television on wiktionary.
The whole issue has been debated here before; I am only posting an answer because Bossinique's answer is unsubstantiated and very misleading, and Carolyn's unsubstantiated and somewhat misleading.
In the Types of things vs. types of thing thread (Types of things vs. types of thing), there is a more reasoned discussion than the above; the bottom line (in both senses) from eric.cheung being
He adds substantiating statistics concerning the acceptability of the different usages.
I'll just add a thought - there is a discussion at the linked thread about whether the noun following 'kinds of' being mass or count makes a difference. I'm sure it can, but with many nouns having dual existences (What kinds of men do you meet in your job? Charles Darwin on the Races of Man.) - the difference not always clear-cut from a semantic viewpoint - the issue is not easily resolved. In addition, the 'kinds of' structure is often used with a singular count noun (or what looks more like a count noun than a mass noun): There are now various different kinds of television: LCD, LED, plasma ...
And, included in the first 6 returns for a Google search for "types of microscope":